# stephens999 / ashr

An R package for adaptive shrinkage

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This repository contains an R package for performing "Adaptive Shrinkage."

To install the ashr package first you need to install devtools:

install.packages("devtools")
library(devtools)
install_github("stephens999/ashr")

The main function in the ashr package is ash. To get minimal help:

library(ashr)
?ash

## More background

The ashr ("Adaptive SHrinkage") package aims to provide simple, generic, and flexible methods to derive "shrinkage-based" estimates and credible intervals for unknown quantities $\beta=(\beta_1,\dots,\beta_J)$, given only estimates of those quantities ($\hat\beta=(\hat\beta_1,\dots, \hat\beta_J)$) and their corresponding estimated standard errors ($s=(s_1,\dots,s_J)$).

The "adaptive" nature of the shrinkage is two-fold. First, the appropriate amount of shrinkage is determined from the data, rather than being pre-specified. Second, the amount of shrinkage undergone by each $\hat\beta_j$ will depend on the standard error $s_j$: measurements with high standard error will undergo more shrinkage than measurements with low standard error.

### Methods Outline

The methods are based on treating the vectors $\hat\beta$ and $s$ as "observed data", and then performing inference for $\beta$ from these observed data, using a standard hierarchical modelling framework to combine information across $j=1,\dots,J$.

Specifically, we assume that the true $\beta_j$ values are independent and identically distributed from some unimodal distribution $g$. By default we assume $g$ is unimodal about zero and symmetric. You can specify or estimate a different mode using the mode parameter. You can allow for asymmetric $g$ by specifying mixcompdist="halfuniform".

Then, we assume that the observations $\hat\beta_j \sim N(\beta_j,s_j)$, or alternatively the normal assumption can be replaced by a $t$ distribution by specifying df, the number of degrees of freedom used to estimate $s_j$. Actually this is important: do be sure to specify df if you can.